What is the limit as x approaches 0 of (1-cos(2x))/x ?

The limit as x approaches 0 of (1-cos(2x))/x is 0

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limit as x approaches 0 of (1-cos(2x))/x

x \to 0 lim (\frac{1 - cos ( 2 x )}{x})

0

Solution steps

x \to 0 lim (\frac{1 - cos ( 2 x )}{x})

Apply L'Hopital's Rule

= x \to 0 lim (\frac{2 sin ( 2 x )}{1})

Plug in the value

x = 0

= \frac{2 sin ( 2 \cdot 0 )}{1}

Simplify

\frac{2 sin ( 2 \cdot 0 )}{1} : 0

= 0

What is the limit as x approaches 0 of (1-cos(2x))/x ?
The limit as x approaches 0 of (1-cos(2x))/x is 0